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On the Number of Nodal Domains of Toral Eigenfunctions

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Original languageEnglish
Article number17
Pages (from-to)3027–3062
JournalAnnales Henri Poincare
Early online date28 Mar 2016
Accepted/In press2 Feb 2016
E-pub ahead of print28 Mar 2016
PublishedNov 2016

King's Authors


We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin’s results for random fields and Bourgain’s de-randomisation procedure we establish a precise asymptotic result for “generic” eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions.

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